TY - JOUR
T1 - Banach-Valued Multilinear Singular Integrals with Modulation Invariance
AU - Di Plinio, Francesco
AU - Li, Kangwei
AU - Martikainen, Henri
AU - Vuorinen, Emil
N1 - Publisher Copyright:
© 2020 The Author(s). Published by Oxford University Press. All rights reserved.
PY - 2022/4/1
Y1 - 2022/4/1
N2 - We prove that the class of trilinear multiplier forms with singularity over a one-dimensional subspace, including the bilinear Hilbert transform, admits bounded L p-extension to triples of intermediate operatorname UMD spaces. No other assumption, for instance of Rademacher maximal function type, is made on the triple of UMD spaces. Among the novelties in our analysis is an extension of the phase-space projection technique to the UMD-valued setting. This is then employed to obtain appropriate single-tree estimates by appealing to the UMD-valued bound for bilinear Calderón-Zygmund operators recently obtained by the same authors.
AB - We prove that the class of trilinear multiplier forms with singularity over a one-dimensional subspace, including the bilinear Hilbert transform, admits bounded L p-extension to triples of intermediate operatorname UMD spaces. No other assumption, for instance of Rademacher maximal function type, is made on the triple of UMD spaces. Among the novelties in our analysis is an extension of the phase-space projection technique to the UMD-valued setting. This is then employed to obtain appropriate single-tree estimates by appealing to the UMD-valued bound for bilinear Calderón-Zygmund operators recently obtained by the same authors.
UR - https://www.scopus.com/pages/publications/85127980265
U2 - 10.1093/imrn/rnaa234
DO - 10.1093/imrn/rnaa234
M3 - Article
AN - SCOPUS:85127980265
SN - 1073-7928
VL - 2022
SP - 5256
EP - 5319
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 7
ER -